Question
The price of a computer component is decreasing at a rate of 13% per year. State whether this decrease is linear or exponential. If the component costs $110 today, what
will it cost in three years?
will it cost in three years?
Answers
GPT 3.5
The decrease in price of the computer component is exponential because it is decreasing at a constant percentage rate each year.
To find the price of the computer component in three years, we need to use exponential decay. We can use the formula:
P = P0(1 - r)^t
Where:
P = final price
P0 = initial price
r = rate of decrease as a decimal
t = time in years
Given:
P0 = $110
r = 13% = 0.13
t = 3 years
Plugging in the values into the formula, we have:
P = 110(1 - 0.13)^3
P = 110(0.87)^3
P ≈ 110(0.658)
Therefore, the computer component will cost approximately $72.38 in three years.
To find the price of the computer component in three years, we need to use exponential decay. We can use the formula:
P = P0(1 - r)^t
Where:
P = final price
P0 = initial price
r = rate of decrease as a decimal
t = time in years
Given:
P0 = $110
r = 13% = 0.13
t = 3 years
Plugging in the values into the formula, we have:
P = 110(1 - 0.13)^3
P = 110(0.87)^3
P ≈ 110(0.658)
Therefore, the computer component will cost approximately $72.38 in three years.